The file in question is located in:\Steam\steamapps\common\flight_control_hd\output_log.txt

You can open it and search for 'games'. Behind that is the number of games you played. Be advised, the number of games played is generated at the start of the game itself. So if you start the game, play 10 games and exit the file will say '0 games played'. If you start Flight Control again and close it the file will say '10 games played'.